According to an embodiment, the invention relates to a computer implemented method for grading a pattern from a first size to a second size, the pattern comprising one or more panels, the method comprising the steps of a representation step comprising representing each panel of the one or more panels by a contour, wherein a contour comprises one or more segments, a constraint step comprising imposing constraints on segments for grading to the second size; generating a mesh of each panel of the one or more panels thereby obtaining a first set of meshes; combining the first set of meshes with the constraints into a system of equations; solving the system of equations into a second set of meshes, wherein the contours of the second meshes correspond to the pattern in the second size and representing the contours of the second set of meshes.
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2. The computer implemented method according to claim 1, wherein the determining the one or more contours of the second set of meshes further comprises approximating the one or more contours by parametric curves.
4. The computer implemented method according to claim 3, wherein the one or more contours of the one or more panels are represented by parametric curves comprising the one or more characteristic points.
This invention relates to computer-implemented methods for representing and manipulating geometric shapes, particularly in the context of designing or analyzing structures composed of panels. The problem addressed is the efficient and accurate representation of panel contours, which is critical for applications such as architectural design, manufacturing, and simulation. The method involves representing the contours of one or more panels using parametric curves. These curves are defined by one or more characteristic points, which serve as control points or key points that determine the shape of the curve. The parametric representation allows for precise control over the panel's geometry, enabling adjustments to the shape by modifying the positions of these characteristic points. This approach simplifies the process of designing and modifying complex panel structures while maintaining geometric accuracy. The parametric curves can be of various types, such as Bézier curves, B-splines, or NURBS (Non-Uniform Rational B-Splines), depending on the application requirements. The characteristic points may include endpoints, control points, or other significant points that define the curve's behavior. By adjusting these points, the shape of the panel can be dynamically altered, facilitating iterative design processes. This method is particularly useful in applications where panels must conform to specific geometric constraints or where the shape of the panels needs to be optimized for structural or aesthetic purposes. The use of parametric curves ensures that the representation remains flexible and adaptable, allowing for efficient modifications without losing precision. The invention enhances the ability to model and manipulate panel-based structures in a computationally effi
9. The computer implemented method according to claim 1, wherein the solving the system of equations into the second set of meshes further comprises minimizing a deformation energy of the second set of meshes with respect to the first set of meshes.
This invention relates to computer-implemented methods for processing three-dimensional meshes, particularly in applications such as computer graphics, simulation, or geometric modeling. The problem addressed involves transforming a first set of meshes into a second set of meshes while preserving geometric and physical properties, such as minimizing deformation energy to ensure realistic or stable mesh configurations. The method involves solving a system of equations to generate the second set of meshes from the first set. A key aspect is minimizing deformation energy, which refers to the energy associated with the distortion or stretching of the mesh during transformation. By minimizing this energy, the method ensures that the resulting meshes maintain their structural integrity and avoid excessive deformation, which is critical for applications requiring realistic simulations or visual fidelity. The system of equations may incorporate constraints derived from the first set of meshes, such as vertex positions, edge lengths, or surface normals, to guide the transformation process. The minimization of deformation energy is achieved through optimization techniques, such as numerical methods or iterative solvers, to adjust the mesh vertices while adhering to the constraints. This approach ensures that the second set of meshes retains the desired geometric properties while minimizing unwanted distortions. The invention is particularly useful in fields like computer-aided design, animation, and scientific visualization, where maintaining mesh quality during transformations is essential for accurate modeling and simulation.
10. The computer implemented method according to claim 1, wherein the solving the system of equations into the second set of meshes further comprises morphing the first set of meshes into the second set of meshes.
This invention relates to computer-implemented methods for solving systems of equations in mesh-based simulations, particularly in fields like computational fluid dynamics (CFD) or finite element analysis (FEA). The problem addressed is the computational inefficiency and accuracy limitations when solving such systems using static or rigid mesh structures, which can fail to adapt to dynamic changes in the simulated environment. The method involves generating a first set of meshes representing a physical domain or system, where these meshes are used to discretize the domain for numerical analysis. The system of equations, which may represent physical laws like fluid dynamics or structural mechanics, is then solved using this initial mesh configuration. To improve accuracy and efficiency, the method further includes morphing the first set of meshes into a second set of meshes. This morphing process adjusts the mesh geometry or topology to better align with evolving solution characteristics, such as changes in fluid flow patterns or material deformation. The morphed second set of meshes is then used to refine the solution of the system of equations, leading to more accurate and computationally efficient results. The morphing step may involve techniques like mesh smoothing, remeshing, or adaptive mesh refinement, ensuring the mesh dynamically adapts to the problem's requirements. This approach enhances the robustness and precision of simulations in dynamic environments.
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December 6, 2018
December 13, 2022
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